A square matrix is a matrix with an equal number of rows and columns. It can be used in various mathematical operations, including solving systems of linear equations.
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A square matrix has dimensions n x n, where n is a positive integer.
The determinant of a square matrix can be calculated and is crucial for solving systems of equations using Cramer's Rule.
A square matrix can be symmetric if it equals its transpose (A = A^T).
The identity matrix is a special type of square matrix with ones on the diagonal and zeros elsewhere.
Invertible matrices are always square matrices, but not all square matrices are invertible.
Review Questions
What criteria must a matrix meet to be considered a square matrix?
How do you determine if a square matrix is invertible?
What role does the determinant play in solving systems of equations using Cramer's Rule?
Related terms
Determinant: A scalar value derived from a square matrix that indicates whether the matrix is invertible. It is used in calculating solutions to systems of linear equations.
Identity Matrix: A special type of square matrix with ones on the diagonal and zeros elsewhere. It acts as the multiplicative identity in matrix multiplication.
Inverse Matrix: A matrix that, when multiplied by its original square matrix, yields the identity matrix. Only non-singular (invertible) matrices have inverses.